This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Presented is a study in which students' intellectual reasoning development was evaluated following instruction that emphasized formal operations in a traditional lecture format. Results indicated that formal-operational students had significantly more success in the three reasoning areas than transitional students and transitional students had…

The purpose of this study was to investigate the relationship between the achievement of some abstract concepts in "molecular genetics" and prior knowledge, formal reasoning ability, and sex. The major findings of the study were: (1) prior knowledge had a high significant correlation with the achievement of abstract concepts; (2) the…